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Theme: mental strategies for addition and subtraction (addition and subtraction progression document) framework document Objectives from the new framework: Reception: Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’ Year 1: Recognise that addition can be done in any order and use this to add mentally a one-digit number or a multiple of 10 to a one-digit or two-digit number Subtract one-digit numbers from one-digit and two-digit numbers and a multiple of 10 from a two-digit number; apply addition and subtraction strategies, e.g. counting on to find the difference Year 2: Add or subtract mentally a single-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to support addition and subtraction of two-digit numbers Year 3: Add or subtract mentally combinations of one-digit and two-digit numbers Year 4:Add or subtract mentally pairs of two-digit whole numbers, e.g. 47 + 58, 91 – 35 Year 5:Use mental methods to add and subtract 2 or more 2, 3 or 4 digit numbers-special cases, e.g. look for number bonds to 10/100 or count on when subtracting numbers near multiples of 100, 1000, e.g. 1995 from 6007 Year 6: Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t Year 6 extension: Consolidate and extend mental methods of calculation Key Resources / Year Target Group Target Outcomes Models and Images Add and subtract numbers Unit plans: Most pupils should be able to: Put 1, 2 or 3 in each circle so that each below 10 Autumn unit 4 What is seventeen subtract five? side adds up to 5. You can use each Yr 1 m Autumn unit 9 number as often as you like. Spring unit 3 Add five and eight? Find different ways of doing it. Add and subtract numbers How many different ways can you score 4 by Calculate below 20 ICT files rolling two dice? What about 6? efficiently and s accurately Excel files Explain strategy for solving: Add or subtract mentally a 4 + 7; 5 add 6; 11 subtract 4; 18 + 5;9 less than 17; Further Problem solving 12 minus 8 examples of single-digit number or a multiple of 10 to or from any materials: pitch and Add or subtract without crossing 10/20 boundaries, expectations: two-digit number; Lisa has 5 pens and Tim has 2 pens. Gobstopper e.g. solve problems such as : How many pens do they have altogether? Bens numbers How many more pens has Lisa than Tim? Foundation to Caterpillar sequences - 3 = 4, 17 - = 12 year 1 Down path Anil spent 6p and 3p on toffees. Lollipops Put the numbers 1 to 4 in the circles so that the What change from 10p did he get? Further Bowling difference between each pair of joined numbers is examples of Pick a pair more than 1. pitch and It is 5 o’clock. expectations: What time will it be 4 hours from now? What time was it 3 hours ago? 20 Bead strings Look at these cards. If you had tea at 3 o’clock, how long ago Year 1 Stories (e.g. Walter’s 3 1 4 2 6 was that? Windy Washing line by If you go to bed at 8 o’clock, how many Further Neil Griffiths) Information hours until bed time? Use one card each time to make these correct. - Divide and c Number lines rule1 Number tracks 7 + = 10 (including those - Divide and marked on the rule2 playground) - = 10 4 Carpet Tiles - teaching 100 Bead bar mental Tick ( ) two numbers which add up to 17. calculation strategies 5 How many children did we ask? - teaching How many children liked more children written 8 6 liked chocolate than lime? strategies 9 - exemplification of standards Level 1b-1a Add and subtract numbers Unit plans: Most pupils should be able to: My cat is 30 cm tall. below 20 Autumn unit 3; Autumn My dog is 25 cm taller. Yr 2 m unit 9 How tall is my dog? Spring unit 3; Summer Quickly solve: unit 9 James walked from 9:45 until 10:15. Calculate Add or subtract mentally a 20 Bead strings 5+36 For how many minutes did he walk? efficiently and single-digit number or a Carpet Tiles 1 + + 5 = 17 accurately s multiple of 10 to or from any Number lines & number 58+21 Which two/three numbers could have a two-digit number; tracks (including those 70-11 sum of 15? Add or subtract mentally marked on the 35+19 Further playground) 24-9 Work mentally to complete written examples of combinations of one-digit and two-digit numbers questions like: pitch and 32 + 5 = ▲; 32 + ▲ = 37; ▲ + 5 = 37 expectations: ICT files Explain how they solved: 86 – 4 = ▲; 86 – ▲ = 82; ▲ – 4 = 82 82-79 Year 2 Problem solving 40+39 30 + 4 = ▲; 30 + ▲ = 34; ▲ + 4 = 34 materials: 600 + 7 = ▲; 600 + ▲ = 607; Further Given 3 numbers, e.g. 2, 7 and 9, be able to say or write▲ + 7 = 607 four Information Gobstopper different number sentences linking the numbers. and explain method. - Divide and Bens numbers rule1 Caterpillar sequences Using three dice, find different ways of scoring 12. Down path Work mentally to complete written - Divide and Lollipops Put the numbers 1 to 5 in the circles so that the questions like: rule2 Bowling difference between each pair of joined numbers is 22 – 17 = ▲ 19 + ▲ = 22 Pick a pair more than 1. 103 – 96 = ▲ 95 + ▲ = 101 - teaching Money match 64 – 58 = ▲ 87 + ▲ = 94 mental Bird eggs calculation Card sharp This table shows how the children in a strategies Monster class come to school. c Sum up Ways of coming Number of - teaching Timetables Respond to oral questions like: to school children written In a line What must be added to 30 to make 100? strategies and explain method. Number square • Work mentally to complete written questions like: walk 14 - exemplification mystery 40 + ▲ = 100 70 + ▲ = 100 of standards Beanbag buckets Lucy Fair I have £14. I am given another £9. taxi 1 Cross roads How much do I have now? Duck pond Christmas candles bus 6 • A pear costs 15p more than an apple. Goldfish problem An apple costs 12p. What does a pear cost? car 8 100 Bead bar 100 Bead strings Investigate ways of using silver coins to pay 50p. (a) More children walk than come by bus. Laminated empty How many more? number lines and (b) How many children are in the class whiteboard pens. altogether? Level 2c-2b Key Resources / Year Target Group Target Outcomes Models and Images Add or subtract mentally a Springboard 3 unit 6 Most pupils should be able to: single-digit number or a Y3 Autumn unit 2; What is twenty-seven subtract nine? multiple of 10 to or from any Y3 Autumn unit 3; two-digit number; Y3 Spring unit 2 Add thirty-six and seventy ICT files What is twenty-six more than fifty? Problem solving Subtract thirty-two from seventy. materials: Yr 3 m The difference between a number and twenty- This table shows the increase in bus fares. Arithmagons nine is ten. What could the number be? Card tricks Esmerelda coins What is the sum of twenty-three and twenty- Crackers seven? Coin rows Sheepdog trials In a class there are thirty-two children. If there Three monkeys are twenty-three girls, how many boys are Odds and evens there? Number square mystery In a class of thirty-two children, fourteen Calculate Add or subtract mentally walked to school and the rest came by bus. efficiently and s combinations of one-digit and Snakes and ladders How many came by bus? accurately two-digit numbers Sohan's new bus fare is 72p. How much has Add or subtract mentally pairs Circle three numbers that add to make a his bus fare gone up? Further of two-digit whole numbers Hundred square multiple of 10. Millie says, 'My bus fare has gone up by 10p'. examples of including crossing the How much is Millie's new bus fare? pitch and hundreds boundary, e.g. 47 + 100 Bead bar 11 12 13 14 15 16 17 18 19 expectations: 58, 101 – 35 100 Bead strings Put a number in the box to make this correct. Each side of this square must add up to 80. 32 + 6 = 40 - ▲ Year 3 Laminated empty Write in the missing numbers. Further number lines and Information Some children made a bar chart to show whiteboard pens. how far they could swim. - Divide and rule1 Calculation course link Sue - Divide and Ann c rule2 Kay - teaching Mark mental This is a number triangle with some numbers calculation missing. The numbers along each edge must Paul strategies add up to 90. 10 20 30 40 50 60 70 80 90 100 - teaching Put all the numbers 20, 30, 50 and 60 in the metres written circles to make the totals correct. Sue can swim further than Anne. How strategies much further? - exemplification of standards Level 2a-3c Add or subtract mentally Autumn: unit 2(1-3); Most pupils should be able to: A box holds 70 biscuits. combinations of one-digit and unit 2(4-5); unit 3(1-2); How many biscuits are left if you eat 17 Yr 4 m two-digit numbers unit 3(3-5); unit 12 Carry out calculations efficiently and explain biscuits? Spring: unit 2; unit 3 methods, e.g. How many people can have 5 biscuits each? Summer: unit 2; unit 3; How many biscuits are there in 6 boxes? Calculate Add or subtract mentally pairs unit 12 49 + 57; 9 + 7 = 16 and 40 + 50 = 90, so 90 + How many boxes are needed to hold 200 biscuits? efficiently and of two-digit whole numbers 16 is 90, 100, 106. accurately s including crossing the ICT files Two shelves are 75 cm and 87 cm long. hundreds boundary, e.g. 47 + 65 – 28 65 – 30 is 35, but this takes away 2 What is their total length in metres? Further 58, 101 – 35 Problem solving too many, so add back 2 to make 37. What is the difference in their lengths in examples of Use mental methods to add materials: centimetres? pitch and and subtract 2 or more 2, 3 or 102 + 295 There are three hundreds and 90 expectations: 4 digit numbers-(special Arithmagons and 7, that’s 397. Raiza got into the pool at 2:26. She swam until cases, e.g. look for number Card tricks 3 o’clock. Year 4 bonds to 10/100 or count on Esmerelda coins 500 – 180 Take away 200, that’s 300, add 20 How long did she swim? Further when subtracting numbers Crackers is 320. Information near multiples of 100, 1000, Coin rows find the missing number in: - Divide and e.g. 1995 from 6007) Sheepdog trials Extend to calculations that cannot entirely be 91 + ▲ + 48 = 250 rule1 Three monkeys done mentally. Three digits For example: • find all the different totals you can make by - Divide and Add to 100 447 + 165 447 + 100 = 547 using three of these five numbers: rule2 More differences 547 + 60 = 607 219, 193, 74, 156, 97 Sum fun 607 + 5 = 612 - teaching Kierons cats • 93 take away 8… Take 7 from 62… mental Presents 3 Arrange the numbers 1, 2, 3... to 9 in the • 63 subtract 46… Subtract 120 from 215… calculation Magic square circles so that each side of the square adds up • 170 less than 250… 1000 less than 5437… strategies Shape puzzle to 12. • What must I take from 84 to leave 26? Number square • What is the difference between 28 and 65? - teaching mystery • How many more than 234 is 249? written • How many less than 68 is 42? strategies c Snakes and ladders • What must I add to 54 to make 93? • Decrease 72 by 34. - exemplification Laminated empty • 28 add a number is 43. What is the number? of standards number lines and • Find pairs of numbers with a difference of whiteboard pens. 79… Solve number puzzles: for example, work out mentally by counting up from the • Each ▲ represents a missing digit. smaller to the larger number: a. Choose three digits from this set: 1, 3, 4, 8. Replace each u to make this statement true: 92 – 89, 403 – 386, 4000 – 3993 ▲▲ – ▲ = 38 b. Find the missing digits. Add mentally: 4▲ + ▲8 = 74 • several small numbers, such as 3 + 5 + 7 + 2 3▲ – ▲9 = 9 + 9; • three multiples of 10, such as 80 + 70 + 40. 3▲ + ▲7 = 120 work out mentally that: I think of a number, then subtract 18. 7003 – 6988 = 15 by counting up 2 from 6988 The answer is 26. to 6990, then 10 to 7000, then 3 to 7003. What was my number? Level 3b Theme: Written methods for subtraction Key Resources / Year Target Group Target Outcomes Models and Images Add or subtract mentally pairs Autumn: Unit 11 Most pupils should be able to: of two-digit whole numbers, Spring: Unit 9; unit 10 Yr 5 e.g. 47 + 58, 91 – 35 Summer: unit 11 • 3754 add 30… Add 700 to 9764… • 18 add 30 add 29… Add 250, 60, 40, 150 and Springboard 5 unit 7 3… Use mental methods to add Springboard 5 unit 8a • What is the sum/total of 226 and 39? Calculate and subtract 2 or more 2, 3 or • How many altogether are 121 and 345? efficiently and 4 digit numbers-(special ICT files • Increase 190 by 37. Write a number in each circle so that the accurately cases, e.g. look for number • Which three numbers could have a total of number in each square box equals the sum bonds to 10/100 or count on Problem solving 450? of the two numbers on either side of it. Further when subtracting numbers materials: Are there any others? examples of near multiples of 100, 1000, • I cut 65 cm off 3.5 metres of rope. pitch and e.g. 1995 from 6007) Joins How much is left? Respond rapidly to oral or written questions, expectations: Calculate mentally with whole Moneybags explaining the strategy used. For example: numbers and decimals, e.g. Three digits • 127 take away 35… Take 80 from 373… Dad bought a 2 kg bag of carrots. Year 5 U.t ± U.t He used 400 grams of carrots to make some Albert square • 678 subtract 105… Subtract 50 from 225… Arithmagons 2 • 500 less than 720. soup. Further How many grams of carrots Magic square • What must I take from 220 to leave 55? Information were left? Magic lines • What is the difference between 155 and 390? - Divide and Pyramids • How many more than 952 is 1050? rule1 200 ml more water is poured Kierons cat • How many less than 305 is 94? Presents 3 • What must I add to 720 to make 908? into the cylinder. - Divide and Mark the new water level. Shape puzzle • Decrease 92 by 78. rule2 • 570 add a number is 620. What is the number? Snakes and ladders • Find pairs of numbers with a difference of - teaching Solve addition and subtraction Long jump challenge 599… mental Pole climber problems in time table context calculation Swimming race strategies • 705 – 287, 8006 – 2993 Laminated empty 1.5 + 1.6 = 3.1 double 1.5 plus 0.1. - teaching number lines and written whiteboard pens. strategies Continue to add/subtract 9, 19, 29… or 11, 21, 31… by adding/subtracting 10, 20, 30… then - exemplification adjusting of standards by 1. • How many Given the numbers 135, 228 and 363, say or matches in write four different sentences relating these total did numbers. Rovers play? Add mentally: • several small numbers, such as 3 + 5 + 7 + 2 + 9; In how many of their matches did Rovers • three multiples of 10, such as 80 + 70 + 40. score more than 3 goals? Level 3a-4c Use mental methods in special Autumn: unit 11 Most pupils should be able to: Calculate the third cases, e.g. to subtract 1995 Spring: unit 7 • Add 4250 to 3536… 66 add 314 add 750… Yr 6 from 6007 Summer: unit 2; • Add 1200, 400, 600, 1200 and 15. angle of a • What is the sum/total of 753 and 227? triangle, given the Springboard unit 12 And of 93, 62 and 25? Calculate Calculate mentally with whole Springboard unit 13 • How many altogether are 854 and 622? other two. efficiently and numbers and decimals, e.g. And 91, 88 and 6? accurately U.t ± U.t • Increase 250 by 420. ICT files Which three numbers could have a total of 1? Further Respond rapidly to oral or written questions, examples of Consolidate and extend mental methods of calculation Problem solving explaining the strategy used. For example: pitch and materials: • 750 take away 255… Take 300 from 1240… Calculate angles expectations: • 3500 subtract 2050… Subtract 2250 from 8500… at a point. Joins • What must I take from 8.4 to leave 2.6? Year 6 Moneybags • What is the difference between 2.2 and 6.5? Three digits • How much more than 23.4 is 24.9? Some children ran in two races on sports Further Albert square • How much less than 6.8 is 4.2? day. Here are their times. Information Age old problems • What must I add to 5.4 to make 9.3? - Divide and Franco’s fast food • Decrease 5.6 by 1.9. rule1 Make 200 • 2.8 add a number is 4.3. What is the number? P+Q • Find pairs of numbers with a difference of 13.5… - Divide and Arithmagons 2 rule2 Magic square • 8000 – 2785 is 15 + 200 + 5000 = 5215 Magic lines - teaching Shape puzzle • 421 + 387 = 808 mental double 400 plus 21 minus 13. calculation ICT games strategies Long jump challenge Add/subtract 0.9, 1.9, 2.9… or 1.1, 2.1, 3.1… In the 800m race, how many seconds did Pole climber by adding or subtracting 1, 2, 3… then adjusting Barry finish ahead of Elise? - teaching Swimming race by 0.1. written The first two numbers in this sequence strategies Laminated empty Add mentally three or more multiples of 10, such as are 2.1 and 2.2. The sequence then number lines and 80 + 70 + 40 + 90. follows the rule ‘to get the next - exemplification whiteboard pens. number,add the two previous numbers of standards Leon and Sara each started with different numbers. ‘ Write in the next two numbers in the sequence. 2.1, 2.2, 4.3, 6.5, , Calculate the perimeters and areas of compound shapes that can Leon and Sara both get the same answer. be split into What numbers could they have started with? rectangles. For example, find the perimeter /area of The temperature is –5 °C. It falls by 6 degrees. this shape. What is the temperature now? Level 4b-4a Consolidate and extend Autumn: unit 11 Some pupils could: Liam has two rectangular tiles like this. mental methods of calculation Spring: unit 7 Springboard unit 12 Springboard unit 13 ICT files Problem solving How long does the first train from Edinburgh materials: Yr 6 take to travel to Inverness? Joins What is the perimeter of Liam’s L shape? Further A sequence starts at 500 and 80 is subtracted Moneybags examples of each time. Three digits A drink and a box of popcorn together cost pitch and Albert square 500 420 340 ... 90p. expectations: Age old problems Franco’s fast food Year 6 into year The sequence continues in the same way. Make 200 7 P+Q Write the first two numbers in the sequence Arithmagons 2 Further which are less than zero. Magic square 2 drinks and a box of popcorn together costs Information Magic lines Megan makes a sequence of numbers starting £1.45. - Divide and K+m+n rule1 with 100. Shape puzzle She subtracts 45 each time. Laminated empty - Divide and Write the next two numbers in the sequence. number lines and rule2 whiteboard pens. 100 55 10 … What does a box of popcorn cost? - teaching Long jump challenge mental Calculate 15.05 – 14.84 Pole climber n stands for number. Match the equivalent calculation Calculate 8.6 – 3.75 Swimming race expressions. One has been done for you. strategies Circle the two numbers which add up to 1. - teaching k, m and n each stand for a whole written 0.1 0.65 0.99 0.45 0.35 number. strategies Here is a table of temperatures at dawn on the They add together to make 1500 - exemplification same day. of standards Temperatures ºC k + m + n = 1500 London –4º Moscow –6º m is three times as big as n. New York –9º Paris +6º k is twice as big as n. Sydney +14º Calculate the numbers k, m and n. What is the difference in temperature between London and Paris? level 5c-5b